Method and apparatus for characterizing the unknown state of a physical system

Abstract

A method and an apparatus are disclosed for characterizing the unknown state of a physical system having a time varying history, the characterization being made with reference to a known state of like physical systems. A response signature representative of the unknown system state is compared to a standard signature representative of the known system state. The standard signature includes a primary signature comprising a multi-dimensional region within a pre-defined, transformed coordinate system having an inner and outer boundary, and a secondary signature comprising at least one, but preferably two or more isoclines situated within the bounded region. If the response signature lies wholly within the bounded region and does not cross any of the region's isoclines, the system being characterized is deemed to be in the known state. Conversely, if both of these criteria are not satisfied the relative degree of departure of the system in the unknown state from the known system state is predicted using one or more point functions representative of the system being characterized.

What is claimed is: 
     
       1. A machine implemented method for characterizing an unknown state of a physical system with reference to like physical systems in a known state comprising the steps of: obtaining with suitable detecting means a time-varying data signal characteristic of a state of interest from each of a large plurality of physical systems in the known state which are similar to the physical system being characterized;   subjecting each of said time-varying data signals to a non-linear coordinate transformation comprising taking a normalized first intergral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said intergral, and converting said difference to polar coordinates;   constructing a standard signature template representative of the known state from a composite of said transformed data signals, said standard signature template including a primary signature comprising a closed multi-dimensional region within said polar coordinate system having an inner boundary and an outer boundary, and a secondary signature comprising at least one isocline disposed within said region;   plotting said standard signature template using plotting means;   obtaining with said suitable measuring means at least one time-varying data signal characteristic of said state of interest from the physical system being characterized;   subjecting said at least one time-varying data signal to said non-linear coordinate transformation to obtain at least one response signature representative of the unknown state;   plotting said at least one response signature over said standard signature template using said plotting means;   determining whether the system being characterized is in the known state by comparing said at least one response signature plot to the standard signature template by determining whether said at least one response signature plot lies wholly within said closed multi-dimensional region, and whether said at least one response signature plot crosses any of said isoclines situated within said closed multi-dimensional region;   indicating the physical system being characterized as being in the known state if said at least one response signature plot lies wholly within said closed multi-dimensional region and does not cross any of said isoclines situated within said closed region, and if the system being characterized is not in the known state,   evaluating the relative degree of departure of the system being characterized from the known state.   
     
     
       2. A machine implemented method as recited in claim 1 wherein said closed multi-dimensional region is a closed two dimensional region, and said secondary signature is comprised of a plurality of substantially parallel isoclines within said closed region. 
     
     
       3. A machine implemented method as recited in claim 1 wherein the steps of obtaining said standard signature template and said at least one response signature plot are further comprised of subjecting said standard signature template and said at least one response signature plot to a predefined topological transformation so that said standard signature template is in the form of two tangent circles and the visual perceptability of said at least one response signature plot with respect to said standard signature template is enhanced. 
     
     
       4. A machine implemented method as recited in claim 1 further comprising: obtaining with said suitable detecting means a time-varying data signal characteristic of the state of a physical system from each of a large plurality of physical systems not in the known state which are similar to the physical system being characterized;   subjecting each of said time-varying data signals obtained from said similar physical systems not in the known state to said non-linear coordinate transformation;   measuring a plurality of predetermined geometric features of each of said time-varying data signals obtained from said physical systems in the known state and said physical systems not in the known state and of said non-linear transformations of said data signals;   calculating a plurality of standard coordinates from said geometric feature measurements utilizing at least one predetermined point function;   plotting said plurality of standard coordinates, said standard coordinate plot falling into three definable regions, a first of said regions corresponding to physical systems in the known state, a second of said regions corresponding to physical systems not in the known state, a third of said regions being indeterminate;   measuring said plurality of predetermined geometric features of said at least one time-varying data signal obtained from said physical system being characterized and of said at least one non-linear transformation of said data signal;   calculating a plurality of response coordinates from said geometric feature measurements utilizing said at least one predetermined point function;   plotting said plurality of response coordinates over said plot of said plurality of standard coordinates; and   further characterizing said physical system to be characterized as being in the known state if said response coordinates fall within said first region.   
     
     
       5. A machine implemented method as recited in claim 4 wherein the step of evaluating the relative degree of departure of the state of the system being characterized from the known system state comprises the steps of: assigning to said at least one response signature plot either a negative value if said plot lies wholly within said closed multi-dimensional region and does not cross any of said isoclines, a positive value if said plot lies wholly or partially without said closed multi-dimensional region or crosses at least one of said isoclines, or a zero value if said plot's positioning with respect to said closed multi-dimensional region and said isoclines is indeterminate;   assigning a negative value to each of said at least one point functions utilized to calculate said response coordinates falling within said first region, a positive value to each of said at least one point functions utilized to calculate said response coordinates falling within said second region, and a zero value to each of said at least one point functions utilized to calculate said response coordinates falling within said third region,   multiplying said at least one response signature plot value and said at least one point function value by weighting factors selected to achieve a desired detection rate or false positive rate; and   summing said weighted point function and response signature plot values to obtain a number which is a measure of the relative departure of the state of the system being characterized from said known state.   
     
     
       6. A machine implemented method as recited in claim 5 wherein said number is inversely related to the relative departure of the state of the system being characterized from the known state. 
     
     
       7. A machine implemented method for characterizing an unknown state of a physical system with reference to like physical systems in a known state comprising the steps of: obtaining with suitable detecting means a time-varying data signal characteristic of a state of interest from each of a large plurality of physical systems in the known state which are similar to the physical system being characterized;   subjecting each of said time-varying data signals to a non-linear coordinate transformation comprising taking a normalized first intergral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said intergral, and converting said difference to polar coordinates;   constructing a standard signature template representative of the known state from a composite of said plurality of transformed data signals, said standard signature template including a primary signature comprising a closed two-dimensional region within a pre-defined coordinate system having an inner boundary and an outer boundary, and a secondary signature comprising a plurality of substantially parallel isoclines situated within said closed two-dimensional region;   plotting said standard signature template using two dimensional plotting means;   obtaining at least one time-varying data signal characteristic of said state of interest from the physical system being characterized;   subjecting said at least one time-varying data signal to said non-linear coordinate transformation to obtain at least one response signature representative of the unknown state;   plotting said at least one response signature over said standard signature template using said two dimensional plotting means;   comparing said at least one response signature plot to the standard signature template to determine whether said at least one response signature plot lies wholly within said two dimensional closed region or crosses any of said isoclines situated within said two dimensional closed region;   assigning said at least one response signature plot either a predetermined negative weighted value if said at least one response signature plot is wholly within said closed two dimensional region and does not cross any of said isoclines, a pre-determined positive weighted value if said at least one response signature plot lies wholly or partially outside said closed two dimensional region or crosses any of said isoclines, or a zero weighted value if the positioning of said at least one response signature plot with respect to said closed two dimensional region and said isoclines is indeterminate;   obtaining a time-varying data signal characteristic of said state of interest from each of a large plurality of physical systems not in the known state which are similar to the physical system being characterized;   subjecting each of said time-varying data signals obtained from said physical systems not in the known state to said non-linear coordinate transformation;   measuring a plurality of geometric features of each of said time-varying data signals obtained from said physical systems in the known state and of said non-linear transformations of said known state data signals;   calculating and plotting a plurality of point function coordinates representative of systems in the known state utilizing a plurality of pre-defined point functions and said geometric feature measurements obtained from said physical systems in the known state;   measuring said plurality of geometric features of each of said time-varying data signals obtained from said physical systems not in the known state and of said non-linear transformations of said data signals not in the known state;   calculating and plotting a plurality of point function coordinates representative of systems not in the known state utilizing said plurality of pre-defined point functions and said geometric feature measurements obtained from said physical systems not in the known state;   measuring said plurality of predetermined geometric features of said at least one time-varying data signal obtained from said physical system being characterized and of said non-linear transformation of said at least one data signal;   calculating a plurality of point function coordinates representative of the system being characterized utilizing said plurality of pre-defined point functions and said geometric feature measurements obtained from said physical system being characterized;   comparing said point function coordinates for said system being characterized with said point function coordinates for said systems in the known state, and for said systems not in the known state;   assigning each of said point functions for said system being characterized a pre-determined negative weighted value if said coordinates calculated with said point function fall within said plot of said point functions for systems in the known state, a pre-determined positive weighted value if said coordinates calculated with said point function fall within said plot of said point functions for systems not in the known state, or by a weighting factor of zero if said coordinates calculated by said point function fall in neither of said plots;   summing said response signature and said point function weighted values to obtain a number; and   comparing said number to a pre-determined cut-off value to determine if the system being characterized is in the known state.   
     
     
       8. A machine implemented method as recited in claim 7 wherein said standard signature template and said at least one response signature plot are further obtained by subjecting said standard signature template and said at least one response signature plot to a pre-defined topological transformation so that said standard signature template is in the form of two tangent circles and the visual perceptability of said at least one response signature plot with respect to said standard signature template is enhanced. 
     
     
       9. A machine implemented process as recited in claims 1, 4, 5, or 8 wherein the steps of obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of taking electrocardiograms using at least one electrocardiographic lead from a plurality of control subjects and a test subject, respectively, to determine whether said test subject is a candidate for a coronary episode. 
     
     
       10. A machine implemented process as recited in claim 9 wherein four electrocardiographic leads consisting of I, II, V 4  and V 6  are used to take four electrocardiographic traces from each of said control subjects and said test subject. 
     
     
       11. A machine implemented process as recited in claims 1, 4, 5 or 8 wherein the steps of obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording a gait pattern using photographic analysis from a plurality of control subjects and a test subject, respectively, to determine whether said test subject has an abnormal gait indicative of joint dysfunction. 
     
     
       12. A machine implemented process as recited in claim 11 wherein said photographic analysis is comprised of taking video recordings of reflective tags placed on at least one joint of each of said control subjects and said test subject. 
     
     
       13. A machine implemented process as recited in claims 1, 4, 5 or 8 wherein the steps of obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording seismographic traces generated by exploration blasts at a plurality of control drilling sites and a test drilling site, respectively, to determine whether oil or gas is available at said test drilling site. 
     
     
       14. A machine implemented process as recited in claims 1, 4, 5 or 8 wherein the steps of obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording test data produced from testing of a plurality of control products destructively tested and a test product non-destructively tested, respectively, to predict whether said test product is about to fail. 
     
     
       15. A machine implemented process as recited in claims 1, 4, 5 or 8 wherein the steps of obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of recording radar traces using a radar system from a plurality of control targets and a test target, respectively, to determine whether said test target is an actual target. 
     
     
       16. A machine implemented process as recited in claims 1, 4, 5 or 8 wherein the steps of obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of recording sonar traces using a sonar system from a plurality of control targets and a test target, respectively, to determine whether said test target is an actual target. 
     
     
       17. An apparatus for characterizing the unknown state of a physical system with reference to like physical systems in a known state comprising: means for measuring a plurality of time-varying data signals characteristic of a state of interest from a plurality of physical systems in the known state, and at least one time-varying data signal characteristic of said state of interest from the physical system in the unknown state;   means for calculating a non-linear coordinate transformation of said plurality of time-varying data signals obtained from said physical systems in the known state to form a standard signature template representative of the known state, said non-linear coordinate transformation comprising taking a normalized first integral of an absolute value of each said time-varying data signals, subtracting a predetermined function from said integral, and converting said difference to polar coordinates, said standard signature template including a primary signature comprising a closed multi-dimensional region within a polar coordinate system having an inner boundary and an outer boundary and a secondary signature comprising a plurality of substantially parallel isoclines disposed within said region;   means for calculating said non-linear coordinate transformation for said at least one time-varying data signal obtained from said physical system in the unknown state to form at least one response signature plot representative of the unknown state;   means for plotting said standard signature template and for plotting said at least one response signature plot over said standard signature template;   means for comparing said at least one response signature plot to said standard signature template to determine whether the system in the unknown state is in the known state, said comparing means comprising means for determining whether said at least one response signature plot lies wholly within said closed two dimensional region or crosses any of said isoclines situated within said closed two dimensional region;   means for indicating said unknown system as being in the known state if said at least one response signature plot lies wholly within said closed two dimensional region and does not cross any of said isoclines situated within said closed region; and   means for evaluating the relative degree of departure from the known state if the system in the unknown state is not in the known state.   
     
     
       18. An apparatus as recited in claim 17 futher comprising means for subjecting said standard signature template and said response signature plot to a pre-defined topological transformation so that said standard signature template is in the form of two tangent circles. 
     
     
       19. An apparatus as recited in claim 17 further comprising: means for obtaining a time-varying data signal characteristic of the state of a physical system from each of a large plurality of physical systems not in the known state which are similar to the physical system to be characterized;   means for subjecting each of said time-varying data signals obtained from said similar physical systems not in the known state to said predetermined non-linear coordinate transformation;   means for measuring a plurality of predetermined geometric features of each of said time-varying data signals obtained from said physical systems in the known state and said physical systems not in the known state and of said non-linear transformations of said data signals;   means for calculating a plurality of standard coordinates from said geometric feature measurements utilizing at least one predetermined point function;   means for plotting said plurality of standard coordinates, said standard coordinate plot falling into three definable regions, a first of said regions corresponding to physical systems in the known state, a second of said regions corresponding to physical systems not in the known state, a third of said regions being indeterminate;   means for measuring said plurality of predetermined geometric features of said at least one time-varying data signals obtained from said physical system being characterized and of said at least one non-linear transformation of said data signal;   means for calculating a plurality of response coordinates from said geometric feature measurements utilizing said at least one predetermined point function;   means for plotting said plurality of response coordinates over said plot of said plurality of standard coordinates; and   means for further indicating said physical system to be characterized as being in the known state if said response coordinates fall within said first region.   
     
     
       20. An apparatus as recited in claim 19 wherein said evaluating means comprises: means for assigning to said at least one response signature plot either a negative value if said plot lies wholly within said closed multi-dimensional region and does not cross any of said isoclines, a positive value if said plot lies wholly or partially without said closed multi-dimensional region or crosses at least one of said isoclines, or a zero value if said plot's positioning with respect to said closed multi-dimensional region and said isoclines is indeterminate;   means for assigning a negative value to each of said at least one point functions utilized to calculate said response coordinates falling within said first region, a positive value to each of said at least one point functions utilized to calculate said response coordinates falling within said second region, and a zero value to each of said at least one point functions utilized to calculate said response coordinates falling within said third region;   means for multiplying said at least one response signature plot value and said at least one point function values by pre-defined weighting factors; and   means for summing said weighted values to obtain a number which is a measure of the relative departure of the state of the system being characterized from said known system state.   
     
     
       21. An apparatus as recited in claim 17 wherein said calculating means is a microcomputer and said comparing means is a display unit capable of overlaying said standard signature template and said response signature plot for comparison purposes. 
     
     
       22. An apparatus as recited in claim 17 wherein the means for obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for taking electrocardiograms using at least one electrocardiographic lead from a plurality of control subjects and a test subject, respectively, to determine whether said test subject is a candidate for a coronary episode. 
     
     
       23. An apparatus as recited in claim 22 wherein said obtaining means is four electrocardiographic leads consisting of I, II, V 4  and V 6  used to take four electrocardiographic traces from each of said control subjects and said test subject. 
     
     
       24. An apparatus as recited in claim 17 wherein the means for obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording a gait pattern for a plurality of control subjects and a test subject, respectively, to determine whether said test subject has an abnormal gait indicative of joint dysfunction. 
     
     
       25. An apparatus as recited in claim 24 wherein said gait pattern recording means is comprised of means for taking video recordings of reflective tags placed on at least one joint of each of said control subjects and on said test subject. 
     
     
       26. An apparatus as recited in claim 17 wherein the means for obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording seismographic traces generated by exploration blasts at a plurality of control drilling sites and a test drilling site, respectively, to determine whether oil or gas is available at said test drilling site. 
     
     
       27. An apparatus as recited in claim 17 wherein the means for obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording test data produced from testing of a plurality of control products destructively tested and a test product non-destructively tested, respectively, to predict whether said test product is about to fail. 
     
     
       28. An apparatus as recited in claim 17 wherein the means for obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording radar traces using a radar system of a plurality of control targets and a test target, respectively, to determine whether said test target is an actual target. 
     
     
       29. An apparatus as recited in claim 17 wherein the means for obtaining said time-varying data signals from said physical systems in the known state and said physical systems not in the known state and said at least one time-varying data signal from said physical system to be characterized are comprised of means for recording sonar traces using a sonar system of a plurality of control targets and a test target, respectively, to determine whether said test target is an actual target.